gammy 0.4.1

Generalized additive models with a Bayesian twist

Gammy – Generalized additive models in Python with a Bayesian twist

A Generalized additive model is a predictive mathematical model defined as a sum of terms that are calibrated (fitted) with observation data.

Generalized additive models form a surprisingly general framework for building models for both production software and scientific research. This Python package offers tools for building the model terms as decompositions of various basis functions. It is possible to model the terms e.g. as Gaussian processes (with reduced dimensionality) of various kernels, as piecewise linear functions, and as B-splines, among others. Of course, very simple terms like lines and constants are also supported (these are just very simple basis functions).

The uncertainty in the weight parameter distributions is modeled using Bayesian statistical analysis with the help of the superb package BayesPy. Alternatively, it is possible to fit models using just NumPy.

Key features

• Intuitive interface for constructing additive models.
• Collection of constructors such as Gaussian Processes and splines.
• Easily extensible term construction framework,
• Build non-linear (w.r.t. inputs) models of arbitrary input dimension.
• Bayesian prior and posterior of model parameters.
• Statistics such as posterior means, covariances and confidence intervals.

Documentation

A documentation of the package with a lot of code examples and plots: https://malmgrek.github.io/gammy.

Short code examples:

• Polynomial regression
• Gaussian process inference
• Spline inference
• Manifold regression of arbitrary dimension

Installation

The package is found in PyPi.

pip install gammy

Quick glance

Let's try to estimate the MATLAB function from pseudo-random samples that are corrupted with pseudo-random noise.

import matplotlib.pyplot
import numpy as np

import gammy
from gammy.arraymapper import x


# Simulate data
n = 100
input_data = 6 * np.vstack((
    np.random.rand(n),
    np.random.rand(n)
)).T - 3
y = (
    gammy.peaks(input_data[:, 0], input_data[:, 1]) + 4 
    + 0.3 * np.random.randn(n)
)

# Fit a model
gp = gammy.ExpSquared1d(
    grid=np.arange(-3, 3, 0.1),
    corrlen=0.5,
    sigma=4.0,
    energy=0.9
)
model = gammy.models.bayespy.GAM(
    # Define a bivariate Gaussian Process prior with a
    # Kronecker structure
    gammy.Kron(gp(x[:, 0]), gp(x[:, 1])) + gammy.Scalar()
).fit(input_data, y)

err = model.predict(input_data) - y  # Prediction error
err.mean()
# 1.00842e-08
err.std()
# 0.739

# Noise std estimated by the model
np.sqrt(model.inv_mean_tau)
# 0.913

Plot generated with gammy.plot.validation_plot:

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